Automatic physical inference with information maximizing neural networks

Tom Charnock, Guilhem Lavaux, and Benjamin D. Wandelt
Phys. Rev. D 97, 083004 – Published 13 April 2018

Abstract

Compressing large data sets to a manageable number of summaries that are informative about the underlying parameters vastly simplifies both frequentist and Bayesian inference. When only simulations are available, these summaries are typically chosen heuristically, so they may inadvertently miss important information. We introduce a simulation-based machine learning technique that trains artificial neural networks to find nonlinear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). In test cases where the posterior can be derived exactly, likelihood-free inference based on automatically derived IMNN summaries produces nearly exact posteriors, showing that these summaries are good approximations to sufficient statistics. In a series of numerical examples of increasing complexity and astrophysical relevance we show that IMNNs are robustly capable of automatically finding optimal, nonlinear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima. We anticipate that the automatic physical inference method described in this paper will be essential to obtain both accurate and precise cosmological parameter estimates from complex and large astronomical data sets, including those from LSST and Euclid.

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  • Received 10 February 2018

DOI:https://doi.org/10.1103/PhysRevD.97.083004

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsGravitation, Cosmology & Astrophysics

Authors & Affiliations

Tom Charnock*

  • Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis boulevard Arago, 75014 Paris, France

Guilhem Lavaux

  • Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis boulevard Arago, 75014 Paris, France and Sorbonne Universités, Institut Lagrange de Paris, 98 bis boulevard Arago, 75014 Paris, France

Benjamin D. Wandelt

  • Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA; Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis boulevard Arago, 75014 Paris, France; Sorbonne Universités, Institut Lagrange de Paris, 98 bis boulevard Arago, 75014 Paris, France; and Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton, New Jersey 08544, USA

  • *charnock@iap.fr
  • lavaux@iap.fr
  • wandelt@iap.fr

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Issue

Vol. 97, Iss. 8 — 15 April 2018

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